Mathematics 426, Section 201

Introduction to Topology

Department of Mathematics,  Undergraduate Math courses,  University of British Columbia

Instructor

John MacDonald

Text

• James R. Munkres, Topology, Second Edition, Prentice Hall, ISBN 0-13-181629-2 .

I will post all handouts, problem sets, final grades, etc. on the web here.

Topics

1. Topological Spaces, Basis for a Topology, The Order Topology
   
2. The Product Topology on XxY, The Subspace Topology, Closed Sets and Limit Points
   
3. Continuous Functions, The Category of Topological Spaces, The Product Topology
   
4. The Metric Topology, The Quotient Topology, Connected Spaces
   
5. Connected Subspaces of the Real Line, Compact Spaces, Compact Subspaces of the Real Line
   
6. The Countability Axioms, The Separation Axioms
   
7. Normal Spaces, The Urysohn Lemma
   
8. The Urysohn Metrization Theorem, The Tychonoff Theorem, The Stone-Cech Compactifiction
   
9. Homotopy of Paths, The Fundamental Group, Covering Spaces
   
10. The Fundamental Group of the Circle, Retractions and Fixed Points
    
11. Deformation Retracts and Homotopy Type, Fundamental Groups of Some Surfaces
    
12. Student Presentations
    We will not necessarily cover all of the topics listed. The list is also subject to change as the term progresses.

Grading

• There will be a midterm on March 12. This will account for 30% of the course mark.
• There will be homework assignments and/or short quizzes. This will count for 40% of the course mark.
• .Near the end of the term each student will make a class presentation for about 20 min and then hand in a writeup of their presentation. Topics are to be selected after the midterm (during the week of March 15-19). This will count for 30% of the course mark.